Min Sum Path in a Triangle

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

For example, given the following triangle

     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]

The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).